ALGLBRAIC!

A python library and CLI utility for generating libraries of algebraic GLSL functions.

Featuring included generators:

• complex-numbers
• dual-numbers
• quaternions
• clifford-algebras

Examples of generated GLSL code can be found in the examples/ directory.

CLI usage examples

Quaternions

> algl quaternions

Output to a directory

> algl --out ./glsl/ clifford-algebra cga2d '1 1 1 -1'

A more complex example

In this example we use the complex-numbers and clifford-algebra generators together in sequence to generate functions for a Clifford algebra with the complex numbers as its base ring:

> algl --glslify --out ./glsl/ complex-numbers clifford-algebra --base C GAComplex '1 1 1 -1'

The --base option passed to the clifford-algebra generator specifies that the base struct for this Clifford algebra should be C, the name of the struct outputted by complex-numbers.

The --glslify option passed at the beginning creates an index.glsl file with glslify-import directives for importing all of the generated glslify files in the order they were generated.

CLI help

Use the --help option!

> algl --help

> algl <COMMAND> --help

You might be wondering...

What about other algebras?

I made alglbraic with geometric algebra in mind but the underlying library is flexible enough to generate GLSL code for any algebra you can get SymPy to print. If you're interested in other algebras I recommend reading the code in alglbraic/algebras.

What about performance?

The code generated by this library is not optimized in any special way! It just bakes out all of the math into GLSL code. If you find it to be quick that's only because it's running on the GPU and everything is happening in parallel.

Big algebras?

This tool probably isn't a good fit for generic computations of operations for algebras with more than 32 or maybe 64 basis dimensions.

Development

To get started you'll need to install Poetry.

Install dependencies

> poetry shell

followed by

> poetry install

Tests

> pytest

or:

> ptw

Updating snapshots

If you change something in a way that breaks the snapshots, the only way I've found to update them is by carefully deleting the snapshot file for the thing that's changed and re-running pytest.